Green’s Dictionary of Slang

1. a brothel.

1904		Sun. Times (Perth) 13 Mar. 1/1: A local rake grown fond of his bosom friend’s wife took the lady to a Stirling-st. Timothy [...] after the pair had departed the madame of the maison announced that she had lost £160 worth of jewellery.
1938		Smith’s Wkly (Sydney) 26 Feb. 3/4: S.P. book makers and ‘Timothy’ Madames found themselves up against a new racket.
1943		Baker Popular Dict. Aus. Sl. (2nd edn).
1950		‘No. 35’ Argot in G. Simes DAUS (1993).
1967		Kings Cross Whisper (Sydney) xli 4/3: timothies: houses in areas where if the rent is paid two weeks in a row the law calls round to see where the money came from.
1978		D. Stuart Wedgetail View 49: I’m like the proverbial moll in the timothy. You’ve talked me into it [AND].
1983		R. Aven-Bray Ridgey-Didge Oz Jack Lang 9: The hallway of the timothy where they lobbed smelt of chunder and snakes hiss. [Ibid.] 47: Timothy Titmouse (house), place of residence.

2. a prostitute.

1904

Sun. Times (Perth) 3 Apr. 1/1: A pair of Monte Carlo maidens last week hiccoughed drunken indecency around the auditorium [...] their salutations to former clients and opposition Timothies proved the pets to be perfect ladies.